assignment week 5
Frodo
assignment_final.docxStatistical Calculations 5
Statistical Calculations
Jeffree Doerflinger
Instructor: Margarita Rovira
August 22, 2014
1. For assistance with these calculations, see the Recommended Resources for Week One. Data, even numerically code variables, can be one of 4 levels – nominal, ordinal, interval, or ratio. It is important to identify which level a variable is, as this impacts the kind of analysis we can do with the data. For example, descriptive statistics such as means can only be done on interval or ratio level data. Please list, under each label, the variables in our data set that belong in each group.
Nominal
ID
Gender
Gender 1
Ordinal
Degree
Grade
Midpoint
Interval
Salary
Age
Performance Rating
Service
Ratio
Compa
Raise
1. The first step in analyzing data sets is to find some summary descriptive statistics for key variables. For salary, compa, age, Performance Rating, and Service; find the mean and standard deviation for 3 groups: overall sample, Females, and Males. You can use either the Data Analysis Descriptive Statistics tool or the Fx = average and = stdev functions. Note: Place data to the right, if you use Descriptive statistics, place that to the right as well:
Salary
Overall = 45
Male = 52
Female = 38
Compa
Overall = 1.062
Male = 1.056
Female = 1.069
Age
Overall = 35.72
Male = 38.92
Female = 32.52
Performance rating
Overall = 85.9
Male = 87.6
Female = 84.2
Service
Overall = 8.96
Male = 10
Female = 7.92
Standard Deviations
Salary
Overall = 19.20140301
Male = 17.77638883
Female = 18.29389698
Compa
Overall = 0.07682507
Male = 0.083789061
Female = 0.070344699
Age
Overall = 8.251258407
Male = 8.38609961
Female = 8.251258407
Performance rating
Overall = 11.41472375
Male = 8.674675786
Female = 13.59227722
Service
Overall = 5.717713258
Male = 6.357410374
Female = 4.906798005
2. What is the probability for a:
a. Randomly selected person being a male in grade E?
= 25/49*12/49
= 0.1249
b. Randomly selected male being in grade E?
= 10/25
= 0.4
c. Why are the results different?
4. For each group (overall, females, and males) find::
a. The value that cuts off the top 1/3 salary in each group.
Overall = 58
Male = 62
Female = 41
b. The z score for each value.
z = (X - μ) / σ
Overall = (58-45)/19.20 = 0.67708
Male = (62-52)/17.77 = 0.5627
Female = (41-38)/18.29 = 0.1640
c. The normal curve probability of exceeding this score.
Overall = 0.2332
Male = 0.2147
Female = 0.1332
d. What is the empirical probability of being at or exceeding this salary value?
Overall = 0.2525
Male = 0.2214
Female = 0.1564
e. The score that cuts off the top 1/3 compa in each group.
Overall = 1.096
Male = 1.086
Female = 1.096
f. The z score for each value.
z = (X - μ) / σ
Overall = (1.096-1.062)/0.07683 = 0.4425
Male = (1.086-1.056)/0.08386 = 0.3577
Female = (1.096-1.069)/0.07034 = 0.3838
g. The normal curve probability of exceeding this score.
Overall = 0.5675
Male = 0.6523
Female = 0.6277
h. What is the empirical probability of being at or exceeding this salary value?
Overall = 0.5573
Male = 0.6372
Female = 0.5986
i. How do you interpret the relationship between the data sets? What do they mean about our equal pay for equal work question?
The data indicates a higher pay ratio for the male employees than the females. The overall comp scores relationship to the individual is drawn that individuals pay that is not proportional to the work rates. It is evident that the salaries vary for the different work performance rate. Equal pay for equal work relationship does not exist. Equal Pay Conclusions
j. What conclusions can you make about the issue of male and female pay equality? Are all of the results consistent?
The results show non-equality on male and female pays for equal work. The results from the analysis on pay because of performance are not consistent.
k. What is the difference between the salary and compa measures of pay?
The compa measures depend completely on the grade. The higher your pay, the higher the resulting compa value will be in the similar pay grades.
l. Conclusions from looking at salary results
There is no equality and consistency in the pay associated with performance rate, it would show that equal pay for equal work does not again exist. There is no clear trend on salaries from the data
m. Conclusions from looking at compa results
Compa results are dependent on the job grade and the salaries of the individuals.
n. Do both salary measures show the same results?
The salary results do not show the same trend or results
o. Can we make any conclusions about equal pay for equal work yet?
From the data there is no trend for equal pay for equal work, so yes.
